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Evolution of flat-plate wakes in sink flow



Evolution of flat-plate wakes in sink flow has been studied both analytically and experimentally. For such wakes, a similarity solution is derived which considers simultaneous presence of both laminar and turbulent stresses inside the wake. This solution utilizes an additional Reynolds-stress term which represents the fluctuations similar to those in wall-bounded flows, accounting for the fluctuations originating from the plate boundary layer. In this solution, it is shown that the total stress, the sum of laminar and Reynolds shear stresses, becomes self-similar. To investigate the accuracy of the analytical results, the wake of a flat plate located at the centreline of a planar contraction is studied using hot-wire anemometry. Wakes of both tapered and blunt edges are considered. The length of the plates and the flow acceleration number K = 6.25 × 10−6 are chosen such that the boundary-layer profiles at the plate edge approach the self-similar laminar solution of Pohlhausen (Z. Angew. Math. Mech., vol. 1, 1921, p. 252). A short plate in which the boundary layer at the edge does not fully relaminarize is also considered. The development of the turbulent diffusivity used in the analysis is determined empirically for each experimental case. We have shown that the obtained similarity solutions, accounting also for the initial conditions in each case, generally agree well with the experimental results even in the near field. The results also show that the mean velocity of the transitional wake behind a tapered edge becomes self-similar almost immediately downstream of the edge.


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Brown, M. L., Parsheh, M. & Aidun, C. K. 2006 Turbulent flow in a converging channel: effect of contraction and return to isotropy. J. Fluid Mech. 560, 437.
Elliott, C. J. & Townsend, A. A. 1981 The development of a turbulent wake in a distorting duct. J. Fluid Mech. 113, 433.
Elsner, J. W. & Wilczynski, J. 1976 Evolution of Reynolds stresses in turbulent wake-flows with longitudinal pressure gradient. Rozpr. Inz. 24 (4), 699.
Gartshore, I. S. 1967 Two-dimensional turbulent wakes. J. Fluid Mech. 30, 547.
George, W. K. 1989 The self-preservation of turbulent flows and its relation to initial conditions and coherent structures. In recent Advances in Turbulence (ed. George, W. & Arndt, R.Hemisphere New York), p. 39.
George, W. K. 1995 Some new ideas for similarity of turbulent shear flows, In ICHMT Symp. on Turbulence, Heat and Mass Transfer, Lisbon, Portugal.
George, W. K. & Davidson, L. 2004 Role of initial conditions in establishing asymptotic flow behavior. AIAA J. 42 (3), 438.
Ghosal, S. & Rogers, M. M. 1997 A numerical study of self-similarity in a turbulent plane wake using large-eddy simulation. Phys. Fluids 9, 1729.
Hoffenberg, R., Sullivan, J. P. & Schneider, S. P. 1995 Wake measurements in a strong adverse pressure gradient. AIAA J. 95, 912.
Hunt, J. C. R. & Eames, I. 2002 The disappearance of laminar and turbulent wakes in complex flows. J. Fluid Mech. 457, 111.
Johansson, P. V., George, W. K. & Gourlay, M. G. 2003 Equilibrium similarity, effect of initial conditions and local Reynolds number on the axisymmetric wake. Phys. Fluids 15 (3), 603.
Jones, W. P. & Launder, B. E. 1972 Some properties of sink-flow turbulent boundary layers. J. Fluid Mech. 56, 337.
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink-flow turbulent boundary layers. J. Fluid Mech. 428, 1.
Keffer, J. F. 1965 The uniform distortion of turbulent wake. J. Fluid Mech. 22, 135.
Moser, R. D., Rogers, M. M. & Ewing, D. W. 1998 Self-similarity of time-evolving plane wakes. J. Fluid Mech. 367, 255.
Narasimha, R. 1989 Whither turbulence? Turbulence at the crossroads. In Lecture Notes in Physics, Proceedings of a workshop held at Cornell University, Ithaca New York, March 22–24 (ed. Lumley, J.), p. 13, Springer.
Narasimha, R. & Prabhu, A. 1972 Equilibrium and relaxation in turbulent wakes J. Fluid Mech. 54, 1.
Narasimha, R. & Sreenivasan, K. R. 1973 Relaminarization in highly accelerated turbulent boundary layer J. Fluid Mech. 61, 417.
Narasimha, R. & Sreenivasan, K. R. 1979 Relaminarisation of fluid flows. Adv. Appl. Mech. 19, 221.
Parsheh, M. 2001 Flow in contractions with application to headboxes. TRITA-PHT Rep. 2000:16 Doctoral thesis, FaxénLaboratoriet, Royal Institute of technology, Stockholm.
Parsheh, M., Brown, M. L. & Aidun, C. K. 2005 On the orientation of stiff fibres suspended in turbulent flow in a planar contraction. J. Fluid Mech. 545, 245.
Pohlhausen, K. 1921 Zur näherungsweisen Integration der Differentialgleichung der laminaren Grenzchicht. Z. Angew. Math. Mech. 1, 252.
Prabhu, A. & Narasimha, R. 1972 Turbulent non-equilibrium wakes. J. Fluid Mech. 54, 19.
Prabhu, A., Narasimha, R. & Sreenivasan, K. R. 1974 Distorted wakes. Adv. Geophys. 18B, 317.
Rogers, M. M. 2002 The evolution of strained turbulent plane wakes. J. Fluid Mech. 463, 53.
Rogers, M. M. 2005 Turbulent plane wakes subjected to successive strains. J Fluid Mech. 535, 215.
Spalart, P. R. 1986 Numerical study of sink flow. J. Fluid Mech. 172, 307.
Sreenivasan, K. R. 1982 Laminariscent, relaminarizing and etransitional flows. Acta Mech. 44 1.
Subsanchandar, N. & Prabhu, A. 1998 Analysis of turbulent near-wake development behind an infinitely yawed flat plate. Intl J. Non-Linear Mech. 33, 1089.
Talamelli, A., Fornaciari, N., Westin, K. J. & Alfredsson, P. H. 2002 Experimental investigation of streaky structures in a relaminarizing boundary layer. J. Turbul. 3, 1.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
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